THE PROBLEM STATEMENT:

A triply charged anion is isobaric with Zn_{65}^{30} and isotonic with an X atom that has a mass number of 70 and whose penultimate electron has the following quantum numbers (n=4; l=0; m=0; s=-1/2). Determine and mark the alternative with the correct nuclear charge of the initial anion.

a) 23. b) 24. c)25. d) 26. e) 27.

THE ATTEMPT AT A SOLUTION:

The problem is to find the nuclear charge (the number of protons) of an incognito anion.

I will call this unknown anion "Y". The statement says "a triply charged anion" that is, Y^{3-}, it is isóbaro (not isobaric) with Zn_{65}^{30}, it means that they share the same mass number.

Then, between 65 and 30, the mass number must be the higher value because A = Z + ºn (mass number is the sum of the number of protons plus the number of neutrons). We have the mass number of the anion in question: Ay = 65.

On the other hand, it tells me that it is both isotonic, (that is not isotonic), with an atom "X" that has a mass number of 70 and whose penultimate electron has the quantum numbers (4,0,0, -1 / 2).

That is to say that: A_{x} = 70.

Then I focus on the data of that penultimate electron: n = 4 (this electron would be in level 4), l = 0 means that we would be in sub-level s. Also m = 0 and s = -1 / 2, then we are in exponent 2. All this leads me to conclude that the electronic configuration must end in 4s^{2}.

Completing the configuration: 1s^{2}, 2s^{2}, 2p^{6}, 3s^{2}, 3p^{6}, 4s^{2}. Add the exponents and reach 20 electrons. But this data belongs to the penultimate electron, then the number that interests me is an atom with 21 electrons. As it must be neutral Z_{x} = 21.

A_{x}=Z_{x}+ºn_{x}

70=21+ºn_{x}

then ºn_{x}=49. That is to say that I have the number of neutrons of the atom "X", which at his view were the same as for the anion "Y" (it was isotonic):

ºn_{y}=49

I can already ask the same equation for the anion in question:

A_{y}=Z_{y}+ºn_{y}

65=Z_{y}+49

Z_{y}=16

That answer is not among the options. Can you help me?

Thanks